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Effect of Buoyancy Force on the Flow Field in a Square Cavity with Heated from Below

Received: 25 January 2017     Accepted: 8 February 2017     Published: 1 March 2017
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Abstract

In this paper, the effect of buoyancy force in a square enclosure is studied numerically. The coupled equations of continuity, momentum and energy are solved by a finite difference method. The SIMPLE algorithm is used to solve iteratively the pressure-velocities coupling. The numerical investigations in this analysis are made over a wide range of parameters, Rayleigh number and dimensionless heater lengths. Results are presented graphically in the form of streamlines, isotherms and also with a velocity profiles and average Nusselt numbers.

Published in International Journal of Discrete Mathematics (Volume 2, Issue 2)
DOI 10.11648/j.dmath.20170202.13
Page(s) 43-47
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Natural Convection, Nusselt Number, Square Cavity, Numerical Simulation, Finite Difference Method, Heat Source, Streamline, Isotherm, Average Nusselt Numbers

References
[1] G. de Vahl Davis and I. P. Jones, “Natural convection in a square cavity: a comparison exercise”, Int. J. Num. Methods Fluid, vol. 3, pp. 227-249, 1983.
[2] S. Ostrach, “Natural convection in enclosures”, J. Heat Transfer, vol. 110, pp. 1175-1190, 1988.
[3] F. A. Kulacki and R. J. Goldstein, “Thermal convection in a horizontal fluid layer with uniform volumetric energy sources”, J. Fluid Mech., vol. 55, pp. 271-287, 1972.
[4] F. A. Kulacki and M. E. Nagle, “Natural convection in a horizontal fluid layer with volumetric energy sources”, J. Heat Transfer, vol. 97, pp. 204-211, 1975.
[5] S. Acharya and R. J. Goldstein, “Natural convection in an externally heated vertical or inclined square box containing internal energy sources”, J. Heat Transfer, vol. 107, pp. 855-866, 1985.
[6] J. H. Lee and R. J. Goldstein, “An experimental study on natural convection heat transfer in an inclined square enclosure containing internal energy sources”, J. Heat Transfer, vol. 110, pp. 345-349, 1988.
[7] Hakan F. Oztop, Eiyad Abu-Nada, Yasin Varol and Ali Chakma, “Natural convection in wavy enclosures with volumetric heat sources”, Int. J. Thermal sciences, vol. 50, pp. 502-514, 2011.
[8] D. a. Neild and A. Bejan, Convection in porous Media, Springer, New York, 1998.
[9] D. B. Ingham and I. Pop, Transport phenomena in porous media, Elsevier, Amsterdam, 1998.
[10] S. Ostrach, Natural convection in enclosures, J. Heat Transfer 110 (1998), 1175-1190.
[11] R. Anderson and G Lauriat, The horizontal Natural convection boundary layer regime in a closed cavity, proceedings of the eight international Heat transfer conference, Vol. 4, San Francisco, CA, 1986, pp, 1453-1458.
[12] Delavar, M. A. and Sedighi, K. [2011] Effect of discrete heater at the vertical wall of the cavity over the heat transfer and entropy generation using Lattice Boltzmann method, Thermal Science, Vol. 15, N, 2, 423-435.
[13] Radhwan, M. and Zaki, G. M. [2000] Laminar natural convection in a square enclosure with discrete heating of vertical walls, JKAU, Eng. Sci., Vol. 12, N°. 2, 83-99.
[14] Varol, Y., Oztop, H. F., Koca, A. and Ozgen, F. [2009] Natural convection and fluid flow in inclined enclosure with a corner heater, Applied Thermal Engineering, 29, 340–350.
[15] Che Sidik, N. A. [2009] Prediction of natural convection in a square cavity with partially heated from below and cooling from SSN -216X Vol. 35 N°3, 347-354. The manuscript number is 147012010.
Cite This Article
  • APA Style

    Md. Noor-A-Alam Siddiki, Ferjana Habiba, Raju Chowdhury. (2017). Effect of Buoyancy Force on the Flow Field in a Square Cavity with Heated from Below. International Journal of Discrete Mathematics, 2(2), 43-47. https://doi.org/10.11648/j.dmath.20170202.13

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    ACS Style

    Md. Noor-A-Alam Siddiki; Ferjana Habiba; Raju Chowdhury. Effect of Buoyancy Force on the Flow Field in a Square Cavity with Heated from Below. Int. J. Discrete Math. 2017, 2(2), 43-47. doi: 10.11648/j.dmath.20170202.13

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    AMA Style

    Md. Noor-A-Alam Siddiki, Ferjana Habiba, Raju Chowdhury. Effect of Buoyancy Force on the Flow Field in a Square Cavity with Heated from Below. Int J Discrete Math. 2017;2(2):43-47. doi: 10.11648/j.dmath.20170202.13

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  • @article{10.11648/j.dmath.20170202.13,
      author = {Md. Noor-A-Alam Siddiki and Ferjana Habiba and Raju Chowdhury},
      title = {Effect of Buoyancy Force on the Flow Field in a Square Cavity with Heated from Below},
      journal = {International Journal of Discrete Mathematics},
      volume = {2},
      number = {2},
      pages = {43-47},
      doi = {10.11648/j.dmath.20170202.13},
      url = {https://doi.org/10.11648/j.dmath.20170202.13},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.dmath.20170202.13},
      abstract = {In this paper, the effect of buoyancy force in a square enclosure is studied numerically. The coupled equations of continuity, momentum and energy are solved by a finite difference method. The SIMPLE algorithm is used to solve iteratively the pressure-velocities coupling. The numerical investigations in this analysis are made over a wide range of parameters, Rayleigh number and dimensionless heater lengths. Results are presented graphically in the form of streamlines, isotherms and also with a velocity profiles and average Nusselt numbers.},
     year = {2017}
    }
    

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  • TY  - JOUR
    T1  - Effect of Buoyancy Force on the Flow Field in a Square Cavity with Heated from Below
    AU  - Md. Noor-A-Alam Siddiki
    AU  - Ferjana Habiba
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    T2  - International Journal of Discrete Mathematics
    JF  - International Journal of Discrete Mathematics
    JO  - International Journal of Discrete Mathematics
    SP  - 43
    EP  - 47
    PB  - Science Publishing Group
    SN  - 2578-9252
    UR  - https://doi.org/10.11648/j.dmath.20170202.13
    AB  - In this paper, the effect of buoyancy force in a square enclosure is studied numerically. The coupled equations of continuity, momentum and energy are solved by a finite difference method. The SIMPLE algorithm is used to solve iteratively the pressure-velocities coupling. The numerical investigations in this analysis are made over a wide range of parameters, Rayleigh number and dimensionless heater lengths. Results are presented graphically in the form of streamlines, isotherms and also with a velocity profiles and average Nusselt numbers.
    VL  - 2
    IS  - 2
    ER  - 

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Author Information
  • Department of Natural Science, Stamford University Bangladesh, Dhaka, Bangladesh

  • Department of Natural Science, Stamford University Bangladesh, Dhaka, Bangladesh

  • Department of Natural Science, Stamford University Bangladesh, Dhaka, Bangladesh

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